How to seperate displacements for different parts of the object?
You're close! But I think this is more what you're after.



Essentially you've got to think of the Checker Texture node as being a 'master-mask' which is used as the Fac input when mixing the other textures together. The black part of the checker will be the top input of the MixRGB node, and the white will be the bottom.

When working with the Displacement node, middle-grey (a value of 0.5) will be no-displacement. This means that you can add the Voronoi Texture to either the top or bottom inputs of the MixRGB node, and as long as you set the other input color to be the middle-grey, and add the Checker Texture mask to the Fac input, then the Voronoi texture will only affect either the white, or black, sections of the mask.





^ Here's a screenshot comparing the difference between applying the Voronoi Texture to the bottom and top inputs of the displacement's MixRGB shader, while using the Checker Texture as the Fac input.

Hope that helps!